solve the equation tanx+secx=2 given that x is greater than or equal to 0 and less than or equal to 2pie

Answers

Answer 1

X = 0.6444

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.

tan x +sec x =2

⇒sin x /cosx + 1/ cos x = 2

⇒1+sin x / cos x  =2

⇒ (sin² x/2 +cos ² x/2 +2 sin x/2 cos x/2 )/( cos ² x/2 - sin²x/2 ) = 2

⇒(cos x/2 +sin x/2)² / ( cos ² x/2 - sin²x/2 ) = 2

⇒( cos x/2+sin x/2)² / (cos x/2 + sin x/2)(cos x/2-sinx/2) = 2

⇒(cos x/2 +sin x/2)/ (cos x/2-sin x/2) = 2

Dividing by cos x/2 in both numerator and denominator,

⇒(1+tan x/2)/(1-tan x/2) =2

⇒ 1 + tan x/2 = 2 - 2tanx/2

⇒ tan x/2 = 1/3

⇒ x= 0.6444

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Related Questions

Which of the following is a trinomial with a constant term?
O A. yo +8y³ +GAY
OB. X
OC. x³ + y
OD. x+ 2y + 10

Answers

Option D x+2y+10 .

A trinomial with a constant term will have three terms, and one of those terms will be a constant, which is a number.

we also know about the Constant

A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

Some relatable terms are :

Monomial: Polynomial having a single term.

Binomial: Polynomial having two terms.

Trinomial: Polynomial having three terms.

In given option we'll define

in option A there is no constant .

option B there i sonly given x which is also not constant.

further in option c it is simply binomial in which only two terms are given without constant .

so at last conclusion is in option D there are three terms are given with one constant which is number 10 .

x+2y+10 is trinomial with a constant.

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Determine the solutions of the equation:

Absolute value of the quantity one fifth times x plus 2 end quantity minus 6 equals two.

x = −50 and x = 30
x = −30 and x = 50
x = −20 and x = 50
x = 30 and x = 10

Answers

Answer:

x = -50 and x = 30

Step-by-step explanation:

Given equation:

[tex]\left|\dfrac{1}{5}x+2\right|-6=2[/tex]

To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:

[tex]\implies \left|\dfrac{1}{5}x+2\right|-6+6=2+6[/tex]

[tex]\implies \left|\dfrac{1}{5}x+2\right|=8[/tex]

Set the contents of the absolute value equal to both the negative and positive value of the number on the other side of the equation, then solve both equations:

Equation 1 (negative value)

[tex]\begin{aligned} &\textsf{Given}: &\dfrac{1}{5}x+2&=-8\\ &\textsf{Subtract 2 from both sides}: \quad & \dfrac{1}{5}x+2-2&=-8 -2\\&\textsf{Simplify}:&\dfrac{1}{5}x&=-10\\ &\textsf{Mulitply both sides by 5}: &5 \cdot \dfrac{1}{5}x&=5 \cdot-10\\&\textsf{Solution}:& x & = -50\end{aligned}[/tex]

Equation 2 (positive value)

[tex]\begin{aligned} &\textsf{Given}: &\dfrac{1}{5}x+2&=8\\ &\textsf{Subtract 2 from both sides}: \quad &\dfrac{1}{5}x+2-2&=8 -2\\&\textsf{Simplify}:&\dfrac{1}{5}x&=6\\ &\textsf{Mulitply both sides by 5}:&5 \cdot \dfrac{1}{5}x&=5 \cdot6\\ &\textsf{Solution}:&x & = 30\end{aligned}[/tex]

Solutions

Therefore, the solutions are:  x = -50 and x = 30.


7. On a recent math test, the boys averaged
81 and the girls averaged 90. If there are twice
as many boys in the class as girls, what was
the overall average for the class?

Answers

“Since the actual number of girls and boys is irrelevant, suppose there is one girl and two boys.

Since the actual scores are also irrelevant, suppose that the two boys got the same score.

Then the girl got a 90 and the two boys got 81 each and

(81 + 81 + 90)/3 = 252/3 = 84.”

Initial estimates of the probabilities of events are known as _____ probabilities.

Answers

Initial estimates of the probabilities of events are known as Prior Probabilities.

Prior Probabilities can be defined as the probability of the event before the event takes place.

For Example ,Let there be three wells X,Y,Z with water in it . it is given that one of the wells have the water that is fit for drinking. So the prior probability that Well Z can have drinking water is 1/3 i.e. 0.333  .

Therefore , the Initial estimates of the probabilities of events are known as Prior Probabilities.

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Which decimals are equivalent to 5x10 + 2x1/100

Answers

Answer:

50.2

Step-by-step explanation:

Solve the equation 29 = v + 23 for v.

Answers

Answer:

6

Step-by-step explanation:

Solving steps

29v+23

Move the terms

- v =23 -29

Calculate

-V=-6

Change the signs

Solution

V = 6

Answer: 6

Step-by-step explanation: the guy above me has the best expanation

find the product of 12 0.6 and 6 1/4

Answers

Find the product by multiplying the numbers = 12 x 0.6 x 6 1/4 = 45

a 65g book is 15cm x 5cm x 3c. Find the density

PLEASE HELP ​

Answers

Answer:

Density=13g/45cm cubed

Step-by-step explanation:

D=M/V

D=65g/225cmcubed

D=13g/45cm cubed

t = 1,000 + 18h

in the equation above, T represents Brittany's total take home pay, in dollars...​

Answers

Answer:

c. 55

Step-by-step explanation:

because if you divide the numbers you'll get this

. The width of a rectangular plot of land is one- quarter of its length. If the perimeter is 360 m, find: a. The length of the land.​

Answers

Answer:144

Step-by-step explanation: so if the width is a quarter of the length, then there are 4 parts to both length sides, plus another 2 parts ( one for each width side), 10parts total.  360/10=36, so 1 part equals 36 for the width, which multiplied by 4 is 144

Plot the y intercept of y=3/2 x-2

Answers

Answer:

(0,-2)

Step-by-step explanation:

That point is the y intercept. (4/3,0) would be the x.

The school finance committee has determined that a $28,000 facilities upgrade will be needed in 12 years. an alumnus has donated $20,000. if invested, will it grow to be enough?

Answers

Answer:

Step-by-step explanation:

QWEQEQWEQEQEQEQ

1.
Write the numbers of dots in the next three steps of
this pattern:
3
6
10
15
2. What i
Answ

Answers

Answer:

your answer is 21

Step-by-step explanation:

The gap between 3 and 6 is 3 the gap between 6 and 10 is 4 the gap between 10 and 15 is 5 so your answer will be 6 more than 15 which is 21

your welcome

Question 3 (1 point)
What is the correct solution for the following addition, reported to the correct
number of significant digits? Assume all numbers are measurements.
3001+ 20.3 +0.009
a) 3021
b) 3021.3
c) 3021.309
d) 3021.30

Answers

Answer:

I think it's C but I'm not 100% sure

The shape below is made of two rectangles joined together.
3 cm
4 cm
6 cm
6 cm
15 cm
Find the total area of the shape.
Optional working
Answer:
+
cm²

Answers

The total area of the shape is 102 cm².

Given that, two rectangles with dimensions L1=15 cm, B1=6 cm, L2=4 cm and B2=3 cm.

What is the area of the rectangle?

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimetres, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle.

We know that, the area of a rectangle = Length × Breadth.

So, the area of rectangle1 = 15 × 6 = 90 cm²

The area of rectangle2 = 4 × 3 = 12 cm²

Total area = 90+12 =102 cm²

Therefore, the total area of the shape is 102 cm².

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Evaluate the function.
ƒ(x) = −3x² + 10x + 13
Find f(-1)

Answers

Answer:

find the inverse of the following function. The Domain and Range of inverse

a) f(×)=× b) f(×)=׳-4

The​ 3-sigma limits for a process whose distribution conforms to the normal distribution includes​ _______ of the observed​ values, in the long run.

Answers

The 3-sigma limits for a process whose distribution conforms to the normal distribution include 99.74% of the observed values, in the long run. This means that if you have a process that is normally distributed, then, in the long run, 99.74% of the values will fall within three standard deviations of the mean.

This is an important concept to understand because it can be used to help control a process. For example, if you know that 99.74% of the values will fall within three standard deviations of the mean, then you can set up control limits that correspond to those values. This can help you ensure that your process stays within the desired range.

Understanding the 3-sigma limits can help you better control your process and ensure that it produces the desired results.

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Given that f(x)=x^2+4x-32f(x)=x
2
+4x−32 and g(x)=x-4g(x)=x−4, find (f+g)(x)(f+g)(x) and express the result in standard form

Answers

Answer: So after solving and simplifying terms equation is[tex]x^4+10x^3-47x^2-360x+1296[/tex]

Step-by-step explanation: Given we have two equations f(x) =[tex]x^{2} +4x-32[/tex] and g(x) = [tex]x-4[/tex]

we have been asked to find ( f +g)(x) that is f(x)+g(x)

So first we add them [tex]x^{2} +4x-32 + x-4[/tex]

So we have an equation that is: [tex]x^{2} +5x-36[/tex]

Then we need to multiply both

[tex](x^2+5x-36)(x^2+5x-36)[/tex]

So we get[tex]\left(x^2+5x-36\right)^2[/tex]

Distribute parentheses

[tex]x^2x^2+x^2\cdot \:5x+x^2\left(-36\right)+5xx^2+5x\cdot \:5x+5x\left(-36\right)-36x^2-36\cdot \:5x-36\left(-36\right)[/tex]

On simplifying

[tex]x^4+10x^3-47x^2-360x+1296[/tex]

So standard form of result is [tex]x^4+10x^3-47x^2-360x+1296[/tex] .

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What is the simplified form of this expression 4(2x-5y)-3x

Answers

Answer:

5x - 20y

Step-by-step explanation:

4(2x - 5y) - 3x ← multiply each term in the parenthesis by 4

= 8x - 20y - 3x ← collect like terms

= 8x - 3x - 20y

= 5x - 20y

Answer:

5x - 20y

Step-by-step explanation:

Hello!

Distribute the terms outside of the parenthesis to the terms inside.

Simplify4(2x - 5y) - 3x4(2x) +4(-5y) - 3x8x - 20y - 3x5x - 20y

The simplified expression is 5x - 20y.

A manufacturer determines that the cost of making a computer component is $4.252525........ Write the repeating decimal cost as a fraction and as a mixed number.

Answers

The fraction is $[tex]\frac{421}{99}[/tex] and the mixed fraction is $4 [tex]\frac{25}{99}[/tex]

The cost of manufacturing computer components is $4.25252525

To find the repeating decimal; cost as a fraction

Since we have two digits repeating decimal place, we multiply 100 and shift two digits

⇒$4.252525×100=$425.252525{using operation multiplication}

Now subtract the original number from this

⇒$425.252525-$4.252525=$421.00000 {using operation subtraction}

Now,

100×(fraction)-(fraction)=$421.00000 {using operation subtraction}

99(fraction)=$421.00000{ using operation division}

The Fraction=$[tex]\frac{421}{99}[/tex]

The mixed fraction is $4 [tex]\frac{25}{99}[/tex]

Therefore, The fraction is $[tex]\frac{421}{99}[/tex] , and the mixed fraction is $4 [tex]\frac{25}{99}[/tex]

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What is the polynomial regression?

Answers

In order to transform linear regression into polynomial regression, certain polynomial terms are added to it due to the non-linear relationship between the dependent and independent variables.

Let's say we have independent data X and dependent data Y. In the preprocessing stage, we turn the input variables into polynomial terms to some extent before feeding the data to a mode.

As a specific example of multiple linear regression, polynomial regression is a type of linear regression that estimates the connection as an nth degree polynomial. The performance can also be negatively impacted by the existence of one or two outliers since Polynomial Regression is sensitive to outliers.

The connection between the dependent and independent variables is best approximated by polynomial. It may be used for a wide range of functions. In general, polynomial suits a large range of curvature.

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Simplify (c4)−5

please please helpppp

Answers

Answer: Reformatting the input :

Changes made to your input should not affect the solution:

(1): "c5"   was replaced by   "c^5".  1 more similar replacement(s).

STEP

1

:

           c4

Simplify   ——

           c5

Dividing exponential expressions :

1.1    c4 divided by c5 = c(4 - 5) = c(-1) = 1/c1 = 1/c

Final result :

 1

 —

 c

Step-by-step explanation: hope this helps

Solve the inequality 5x + 3 ≥ 48

Answers

x≥9
I THINK THIS IS IT

Answer: x[tex]\geq[/tex]9

Step-by-step explanation:

5x+3 [tex]\geq[/tex] 48

5x[tex]\geq[/tex]45

x[tex]\geq[/tex]9

Treat inequalities like normal equations. Only when the right side of the equation is introduced to a negative sign via multiplication or division should you flip the inequality sign

Hope this helps!

Use the Angle Addition Postulate to find the measure of the unknown angle.

Answers

Answer:

Hey there!

Step-by-step explanation:

This is ur answer....

60 + 120 = 180

DEF = 180

Hope it helps!

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6. You just had surgery on your knee. As part of rehabilitation your physical
therapist wants you to walk 1 minute on day 1 and double your time every day. How
many minutes will you be walking on day 7?

Answers

64 minutes

Step-by-step explanation:

1x2=2 it day one

2x2=4 it day two

and more

32x2=64 it day 7

This figure is composed of a parallelogram and a trapezoid.
32 cm
26 cm
40 cm
T
16 cm
1
What is the area of the figure in square centimeters?

Answers

Answer:

944cm²

Step-by-step explanation:

Area = Area of parallelogram + Area of trapezoid

Area of parallelogram= l× b= 16×26= 416cm²

Area of trapezoid= h/2(a+b)

where a=26cm, b=40cm, h=16cm

Area of trapezoid= 16/2(26+40)=8(66)=528cm²

Area= 416+528=944cm²

Play equation 19+0.15p= c gives the cost c in dollars that a store charges to deliver an appliance that weighs p pounds. use the equation and a table to find the weight of an appliance that cost $37 to deliver.
The appliance weighs ?? pounds.

Answers

the appliance weighs 120 pounds.

37-19=18
18/.15=120

Petrina had a piece of red ribbon that measured 2.4 m long. she also had a piece of blue ribbon which was 7 8 m long. what was the total length of both ribbons? round your answer to 2 decimal places.

Answers

The total length of red and blue ribbons is 10.2 m.

Given that, the length of the red ribbon =2.4 m and the length of the blue ribbon =7.8 m.

How to add two decimals?

Adding decimals is similar to the usual addition of whole numbers. We know that a decimal number is a number with a whole number part and a fractional part which is separated by a decimal point.

Now, the length of the red ribbon + the length of the blue ribbon=2.4+7.8

=10.2 m

Therefore, the total length of red and blue ribbons is 10.2 m.

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simplify 2cos3xsin3x
step by step pls

Answers

After simplifying the trigonometric expression 2 cos (3 x) sin (3 x), we get the value as sin (6 x).

We are given the expression as:

2 cos (3 x) sin (3 x)

Now, we know the trigonometric identity as:

2 sin θ cos θ = 2 sin (2 θ)

Using this identity in the expression where θ = 3 x, we get that:

2 cos (3 x) sin (3 x) = sin ( 2 × 3 x) ( value of θ substituted in the expression)

2 cos (3 x) sin (3 x) = sin (6 x)

Therefore, after simplifying the trigonometric expression 2 cos (3 x) sin (3 x), we get the value as sin (6 x).

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Loren already knows that he will have $500,000 when he retires. If he sets up a payoutannuity for 30 years in an account paying 10% interest, how much could the annuity provideeach month?

Answers

The annuity could pay $221.19 per month.

ANNUITY FORMULA: [tex]P_t=\frac{d\left[\left(1+\frac{s}{n}\right)^{n t}-1\right]}{\frac{s}{n}}[/tex]

Where,

[tex]P_t[/tex] is the account balance after t years.The regular deposit (the amount you deposit each year or month) is denoted by d.r denotes the annual interest rate in decimal form.n represents the number of compounding periods in a year.t consider the number of years.

So,

Loren anticipates having $500,000 when he retires.

[tex]P_t[/tex] = $500,000

He establishes a 30-year payout annuity at a 10%interest.

t = 30 years r = (10/100) = 0.1

Each month, the annuity could provide

n = 2

In the formula, replace the above values as follows:

500,000  [tex]=\frac{d\left[\left(1+\frac{1.1}{12}\right)^{(12)(30)}-1\right]}{\frac{11-1}{12}}[/tex]500,000 [tex]=\frac{d\left[(1.00833333)^{300}-1\right]}{0.00833333}[/tex]500,000 = d [2260.487925]

Now, divide both sides by: 2260.487925

d = $221.19

Therefore, the annuity could pay $221.19 per month.

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